Getting around in Mexico City, it's no small task. Most of us are, of course, familiar with traveling by car, being from Iceland that is especially the case, as the public transportation system has really never been up to par with what it should be and what takes you maybe 10-15 minutes by car will take you 40 minutes by bus. So it is no strange thing that I am fascinated by a working public transportation system, coming from an expensive bus, which often is not on time.
In Mexico City you can have a car, and you can quite well go around in. However, often the public transportation will be quicker and more often easier. The city runs on “peseros” (I will define it as a small green and white bus that goes around, most often with a quite crazy driver who seems to be on a Formula 1 track rather than the busy streets of Mexico City, zooming past other drivers, competing with other peseros in who can pick up most people) and the metro-system (metro, metro bus). These are really the backbone of the public transportation system, the peseros take you around with great speed and frequency between your home and the nearest metro station, where in turn you travel through various stations changing where you need to change between one of the 12 lines of the metro (not counting the metro-bus, which is a bus system with dedicated lanes and stations).
Of course there are trade-offs to these methods of traveling, the bus and metro can be dangerous, with many getting robbed or even kidnapped on the way. While the humble private car brings you some peace of security, but anxiety as you have to navigate the vast network of streets in rush-hour traffic to get to your desired location.
Another thing is the safety of the whole system, as some metro lines are not really well maintained, as was seen recently where a metro line was closed down because of an accident.
With technology come other solutions, such as Uber or other driver services. These tend to compete with the local taxis, but are often safer since they are maintained by the app and the drivers and passengers are in constant connection with the system along the way. 100% safe it's not, but safer yes.
I, however, would highly recommend you to use the public transportation system here as, coming from Iceland, it seems to be rather efficient and a very cheap alternative to taxi or a private car. Just be careful and aware of your surroundings, as you should be in any train or metro system in the world, whether it's here, Stockholm, London, or really anywhere.